Improvement in the process of shipping non-perishable goods
Sara Filipa Gonçalves Ascenção
Master Thesis
Supervisor at FEUP: Prof. Américo Azevedo
Supervisor at Jerónimo Martins Retalho: Dr. Nuno Miguel Silva
"A mind that opens to a new idea never returns to its original size."
Abstract
When deciding how to ship goods from warehouses to stores, companies have some challenges to overcome concerning the planning of the best routes and managing the fleet of trucks. Nowadays, it still relies on intuition and lifetime experience of the fleet manager, as they have to take on consideration many variables such as loading and unloading goods; distances between warehouses and stores, driver’s workload and at same time to guarantee a high service level.
This thesis was developed in a practical context, based in a real problem which intends to determine the best method set of routes for shipping different types of non-perishable goods (Just In Time and Stock), from warehouse to the stores. It also cares about providing the daily delivery and to fulfilling the time-window of the stores.
This is a Vehicle Routing Problem (VRP) with Time Windows and a Heterogeneous Fleet with a single depot. In order to minimize costs and guarantee that time-windows of stores are accomplished, we developed a mathematical model and present some heuristics approaches to solve it. We proposed a VRP Spreadsheet Solver that conducted a series of experiments to find a feasible solution. With different combinations of type of fleet, type of goods and time-windows we conclude that the best solution is shipping the two types of goods (Just In Time and Stock) instead of one type at a time.
Acknowledgments
I want to thank to Dr. Nuno da Silva for all his support during internship, his guidelines and kindness.
I’m deeply grateful to everyone from JMR for their care and help, especially to Engineer Joana Moreira, Engineer Jorge Bessa and Engineer Beatriz Barbosa.
Of course, to Manuela, Marta and Rosa for the patience they had in answering all the questions I had, always with a smile on their faces.
A big thank you to the professor Américo Azevedo for guiding, motivating and supporting me during the process of writing the thesis.
Professors Jorge Freire and Jorge Pinho for their interventions and guidelines.
To my friends, especially Teresa Queirós, Pedro Roseira, Mar'ahtus Sholihah and Rui Carneiro, for all the courage, help and for the good times spent together while attending this Master.
To my family: father and mother thank you for supporting me once more in another stage of my academic life; to my lovely sister Joana for all the help, motivation and teachings throughout my life (and there are many!); to my brothers in-laws: Valter (for the jokes and the rides) and Carlos (for the improvements and all the patient); to my grandmother by just being there and to Marianas of my life for being not only the source of my inspiration as a guide to my continuous growth.
A heartfelt thanks to Giuseppe Jordão for helping me finding the light at the end of the tunnel, for all our Skype talks and for the help indeed.
Table of Contents
1 Introduction ... 1
1.1 Context ... 1
1.2 Problem Description ... 2
1.2.1Description of the project context ... 2
1.2.2The project and the specific problem addressed ... 2
1.3 Research questions and Methodology ... 3
1.4 Document outline ... 5
2 Theoretical Background ... 6
2.1 Non-perishables and perishable goods ... 7
2.2 Retail Business ... 7 2.3 Operational Research ... 8 2.4 Presentation of findings ... 12 3 Problem Characterization ... 15 3.1 Company´s Description ... 15 3.2 Routes ... 16
3.3 AS-IS (Current situation) ... 16
3.4 Organization of warehouses facilities ... 17
3.4.1JIT Warehouse ... 18
3.4.2Stock Warehouses ... 19
3.4.3Stores description ... 19
3.4.4Transport Team ... 20
3.5 TO BE situation - New Warehouse ... 21
4 Model Development ... 23
4.1 Quantitative Methodology ... 23
4.1.1Comparative analysis of existing approaches ... 23
4.1.2Method used in the project ... 24
4.2 Problem Formulation ... 25 4.2.1Sets 26 4.2.2Parameters ... 26 4.2.3Decision Variables: ... 27 4.2.4Mathematical Model ... 27 4.3 Method Approaches ... 30 4.3.1Heuristic approaches... 30
4.4 Using VRP Excel Solver ... 34
4.5 Results ... 37
5 Conclusion, limitations and future research... 41
5.1 Conclusion ... 41
5.2 Study Limitations... 42
5.3 Future Research ... 42
References ... 44
APPENDIX A: Gantt Diagram. ... 47
APPENDIX B: Process Map of non-perishable goods. ... 48
APPENDIX C: Vehicle´s Cost (for TJA fleet) ... 49
APPENDIX D: Vehicle´s Cost (for ZAS fleet) ... 50
APPENDIX E: Coordinates (latitude and longitude) of the stores. ... 51
APPENDIX F: Workflow Diagram of warehouses interactions. ... 52
APPENDIX G: Process Map of Manage goods. ... 53
APPENDIX H: Workflow Diagram - Suppliers Arrive at JIT Warehouse. ... 55
APPENDIX I: Process Map - Shipping on JIT warehouse. ... 56
APPENDIX J: Workflow diagram of Operations in Stock Warehouse. ... 57
APPENDIX K: Current Workload of the stores (time-window). ... 58
APPENDIX L: Maximum capacity of truck for each store. ... 62
APPENDIX M: Average of occupation and use of each truck. ... 63
APPENDIX N: Diagram of Relationships between stakeholders, warehouses and transports in the new Warehouse. ... 66
List of Tables
Table 1 – Average of volumes produced in each warehouse. 17 Table 2 – Capacity of the fleet of trucks. 20
Table 3 – Pseudo-code of Priority-based Heuristic (PBH). 31 Table 4 – Ruin and Recreation heuristic approach. 33 Table 5 – A LNS algorithm approach. 34
Table 6 – Results of total cost with transportation using just ZAS fleet. 37 Table 7 - Results of total cost with transportation ZAS and TJA fleets. 37 Table 8 – Results of different combinations of variables. 40
List of Figures
Figure 1 – Research Methodology. 4
Figure 2 – Several steps to find a solution to the problem. 15 Figure 3 – New Warehouse Shipping Process. 22
Figure 4 – Framework of the Spreadsheet for locations. 35 Figure 5 – Framework of distances data. 36
Figure 6 – Framework of the total costs of JIT volumes, without time-windows and using just ZAS fleet. 36 Figure 7 – Geographical descriptions for operation routes of fleet vehicles. 37
List of acronyms, abbreviations and definitions
Acronyms and Abbreviations
2L-HFVRP Two dimensional Loading Heterogeneous Fleet Vehicle Routing Problem
CARP Capacitated Arc Routing Problem
CVRP Capacitated Vehicle Routing Problem
DSS Decision Support System
GA Genetic Algorithms
HMA Hybrid Metaheuristic Approach
HVRP Heterogeneous fleet Vehicle Routing Problem
ILS Iterated Local Search
JIT (logistic term) Just in Time
JMR Jerónimo Martins Retalho
LNS Large Neighborhood Search
LNS Large Neighbourhood Search
MTSP Multiple Travelling Salesmen Problem
QWL Quality of Working Life
RO Robust Optimization
TMS Transport Management System
VBA Visual Basic for Applications
VRLP Vehicle Routing and Loading Problem
VRP Vehicle Routing Problem
VRPPD Vehicle Routing Problems with Pickup and Delivery
Definitions
Terms Definition
Backhauling Refers to the practice of not sending the cargo trucks back empty
rather having them take some cargo from some suppliers in their journey back to the main warehouse.
Distribution Centers Set of warehouses that allows physically separation of the
several categories of goods that exist in the stores.
JIT Just in time system of producing goods is based on preventing waste by producing only the amount of goods needed at a particular time and not paying to produce and store more goods than those needed.
Non-Perishable goods There are two types: food and non-food goods but all of them
have a large expiration date.
Pallets A platform, on which goods can be executed, moved and stored.
Risks boxes Plastic boxes containing small and expensive materials that are
sealed to control that no one open before gets to store.
Rollcontainers Metallic object used to transport goods.
Stock The goods storage in the warehouse until needed for distribution.
Store A place that daily order the goods need, received and store them
to sell to customers.
Warehouse A large building where goods may be stored before they are
1 Introduction
1.1 Context
The routing problems are a well studied subject since the 70s, useful to many different areas such transportation, distribution and logistics, especially in retail companies. Retail companies need to ensure the best routes of their truck fleets to minimize distances and so, minimizing costs. In some situations, the experience of the fleet manager is still the way to best plan the routes and to guarantee the daily distribution to stores.
For that kind of problems is common to use Vehicle Route Problems (VRP), that is a generic name used to several types of problems, but basically is about planning a set of routes for fleet vehicles (homogeneous or heterogeneous) based at depot (one or many) and shipping goods to customers (or stores). So, VRP can help define a set of routes performed by a fleet of trucks and guarantee that each route starts and ends at warehouse at minimum costs.
VRP can be divided into some constraints types as:
Capacitated Vehicle Routing Problem (CVRP), where each vehicle has a limited capacity;
Vehicle Route Problem with Time Window (VRPTW), is a problem that involves a
time-window that each store has and must be insured;
Multi-depot VRP there are several depots to satisfy customers;
Vehicle Routing Problems with Pickup and Delivery (VRPPD), each store has associated two quantities: demands to be delivered and demands to be picked up.
Backhauls VRP, when a demand will be collected, normally, each route starts and ends at warehouse, each store is visited by exactly a single route, but the total demand of backhauls or orders to store can’t exceed separately the vehicle capacity.
These types of problems, with high complexity and data dimensions are classified as a NP-Hard problem which means they require a large computational effort and solutions are hard to find. Therefore approaches such as heuristic algorithms or metaheuristics have proven to be more adequate for finding solutions in an achievable time.
1.2 Problem Description
1.2.1 Description of the project context
The problem studied in this thesis is "Improvement in the process of shipping non-perishable goods" of a retail company and aims to provide new ideas and solutions to minimize their shipping costs. It is a case study in real context of a Portuguese retail company; which intends to find out solutions for the shipment of non-perishable goods (food and non-food). This study was developed while the company is launching a new warehouse, so the model presented in this thesis could help to optimize the shipping process of the new warehouse. The shipping process is connected with warehouses, stores and transport’s team. Hence is necessary to distinguish the two types of current warehouses (JIT and Stock), how they operate individually and jointly, to understand the criteria used to define the routes from the currently warehouses to the stores.
The preparation of this thesis is related to the following objectives:
Understand deeply some processes in Logistics and Operations;
Develop problem-solving skills;
Understand the different layout of Stock and Just in Time´s (JIT) warehouse and their efficient management;
Distinguish the main differences between JIT and Stock´s warehouses;
Identify the critical processes related to the shipping of non-perishable goods;
Identify the inputs and outputs needed to resolution of this problem;
Study different heuristic approaches.
1.2.2 The project and the specific problem addressed
As we set out to study: "Under what conditions should the company ship from the new warehouse to the stores?” is important to ensure a model for the company to conceive and decide on the most viable solution. The problem is based on the route improvement suggestion and optimization of processes in warehouses. So, for that we should study the current processes, routes and time-windows of warehouses and stores and understand whether they are the most appropriate or not.
• Minimize company costs with the shipping process;
• Analyze the advantages of shipping non-perishables (JIT and Stock) together, and create relational synergies with transport’ team;
• Explore the relationship between warehouses, stores and transport on the shipping process. This investigation research is relevant to be conducted since it will have a direct impact on business operations in the company, that provided the physical and human resources which made the research possible and achievable.
1.3 Research questions and Methodology
It is critical to define at this stage, the research questions:
Research Question 1: Should JIT volumes be shipped with the Stock volumes? Research Question 2: Should the company use one or two fleet carriers?
These research questions aim to develop scenarios to optimize the shipping route of non-perishable goods. It is important to minimize the transportations costs while maintaining a high level of service (distributed all demands to the stores). As we will see, it is important for the company to know how to ship their goods. It is more advantageous to unify cargo (JIT and Stock) or ship separately? Since the company has a contract with two carriers trucks, it should realize what brings more benefits: using the two carriers or only one with a larger fleet, because the fixed costs of the carriers are different as we will see in following chapters.
The methodology used in this research was divided into three phases, as shown in figure 1, the first one is background research in which the scope and research questions are defined. The second phase is about literature review about this subject, especially about Vehicle Routing Problems and heuristic approaches topics. The last one is about, the mathematical formulation of the problem, a heuristic approach description, a Spreadsheet VRP to solve it and the results found.
Figure 1 – Research Methodology.
A VRP is an interesting tool for the retail sector because companies can make use of mathematical models to minimize costs by adjusting routes. This study is related to the new needs of shipping and warehouses processes in Jerónimo Martins Retalho (JMR) Company. The development of this project is related to the issue of shipping non-perishable goods while ensuring their deliveries in the exact time-windows of the stores and reducing kilometers traveled by trucks. Each task of this study was planned beforehand in order to promote the
1.4 Document outline
This chapter provides an overview of this document research and makes an introduction to the subject. The remainder of this document includes five further chapters and appendix. The second chapter is related to the state of the art. The third chapter provides an overview of the problem, characterization of the company, its current facilities and description of new warehouse. The fourth chapter presents a mathematical model that mentions the system constraints, assumptions and dependencies, heuristic approaches and a Spreadsheet VRP Solver. The fifth chapter of this document is related to the conclusion of this entire thesis project, the main objectives achieved, study limitations and future recommendations. The end of the document includes the appendix that contain all information collected during this project and because of space limitation couldn’t be integrated in the previous sections.
2 Theoretical Background
The literature review provides a frame of reference to interpret the results; leads to the establishment of hypotheses and guides on how to conduct the study. It is a continuous process, initially more difficult by lack of knowledge of the subject and gradually becomes clearer what we should investigate as theoretical approaches, methodology and data collection techniques are concerned.
This section highlights the state of the art on Vehicle Routing Problems. The purpose of the literature review is to find gaps on the chosen topic. In this way, it contributes to increase the scientific knowledge of the under area study. During this project, we made a research about the subject: Operations Research using Quantitative Methodology as Vehicle Routing Problem in Retail Businesses. A literature review will help to identify the appropriate methodology through comparing different models, as one of the main reasons for conducting
the literature review is to enable researchers to find out what is already known. (Levy &
Ellis, 2006). The literature review helps to strengthen the results obtained during the thesis, and at the same time helps others to acquire knowledge on these topics.
Levy & Ellis (2006) state, doing so will enable the researcher to provide a solid argument for
the need of study as well as their spot where literature fits into their own proposed study. A
crucial step for writing a thesis is to carefully make a quality literature review and know the state of the art about that topic and get as much information as possible. At this point, the main objectives are to explore articles and books that have studied the topic and check the existence of a gap, and then set the research method. We review some former and recent articles using the databases: Scopus, Ebsco and Google Scholar for this research.
Throughout all this process, it is necessary to follow a particular pattern because there are too many articles on this topic. After searching several papers and articles, it should be noted that not all articles show the same quality and rigor, so, taking this into account, we must choose the most relevant. The need arises to catalog and categorize the information of these articles, which can be used to build new knowledge. After reading the articles it is crucial to understand and define the concepts: Non-perishables goods, Operational Research, Vehicle Routing Problems and Heuristics approaches.
2.1 Non-perishables and perishable goods
H.-K. Chen, Hsueh, & Chang (2009), describe perishable goods, such as food goods,
vegetables, flowers, living animals and ready-mix concrete, often deteriorate during the production and delivery processes. More and more suppliers adopt just-in-time production and delivery strategy to fulfill their orders from retailers because they can reduce the loss of their own profit due to deterioration of perishable goods. While perishables have to take
account their shorter shelf life period (counting from the day it is produced and the day it is no longer acceptable to consume), non-perishables have a longer shelf life. Amorim, Günther, & Almada-Lobo (2012), study for a production and distribution problem of perishable goods, and realize that, the logistic setting of our operational problem is multi-product, multi-plant,
multi-DC and multi-period and is a fixed shelf-life it most have an integrated model, the integrated production and distribution planning of perishable goods with fixed shelf-life (PDP-FSL) may be formulated as a multi-objective mixed-integermodel.
Govindan, Jafarian, Khodaverdi, & Devika (2014), propose other approach to ship perishable food, a multi-objective optimization model by integrating sustainability in decision-making,
on distribution in a perishable food supply chain network and it introduces a two-echelon location–routing problem with time-windows. Although the goods have different expiration
dates, the JIT layout of non-perishable goods requires also a reception, execution and delivery just 24 hours in the warehouse, such as the perishables. To our knowledge, there is a gap in studies about shipping of non-perishables goods in a retail businesses.
This study is based on the real case of a retail company, so it is important to define and explain the main activities of a retail business.
2.2 Retail Business
According to Sorescu, Frambach, Singh, Rangaswamy, & Bridges (2011), a retail business
model articulates how a retailer creates value for its customers and appropriates value from the markets. Innovations in business models are increasingly critical for building sustainable advantage in a marketplace defined by unrelenting change, escalating customer expectations, and intense competition. It is important to a company invest time and money to better
understand the way that warehouses and stores operated, their layouts, shelf allocations, and with that make changes in order to increase profits.
The next topics to be addressed are related to a very wide and discussed in scientific area – Operational Research.
2.3 Operational Research
2.3.1 Robust Optimization (RO)
Opher Baron, Joseph Milner (2010), study a robust optimization to the problem of locating
facilities, consider a variant of the capacitated fixed-charge multi-period facility location problem where the production capacity of each facility must be determined before observing demand during the horizon.
In a robust approach, minimax-regret and minimax-cost are applied. Baron realizes that the robust model with the box uncertainty performs poorly with respect to balancing robustness with profit. In contrast, the model with the inscribed ellipsoid provides small but significant improvements in the average profit. And most important, that a single ellipsoid is able to provide good solutions over a wide range of parameter choices.
Based on these models and their uncertainty, the manager must be able to take an option, according to Gabrel, Murat, & Thiele (2012), must determine what it means for him to have a
robust solution: is it a solution whose feasibility must be guaranteed for any realization of the uncertain parameters? Or whose objective value must be guaranteed? Or whose distance to optimality must be guaranteed? The main paradigm relies on worst-case analysis: a solution is evaluated using the realization of the uncertainty that is most unfavorable. This author
specific the applications of Robust Optimization in several areas, which he considers using RO in a combinatorial optimization or scheduling problems.
2.3.2 Vehicle Routing Problem (VRP) – Definition
VRP was introduced by Dantzig & Ramser (1959), as an approach of Traveling Salesman Problem (TSP). VRP represents distances, travel cost and times, normally V0 is the origin called depot (warehouse) and V represent the customer (or stores) that want to be served. So VRP tries to define a set of routes for k vehicles that start at depot and visit customers exactly once, that minimize the routing costs.
After Dantzig and Ramser, several studies report some modifications, VRP is classified as NP-hard problem because its variants, so there is: CVRP that treat vehicles with finites capacity; VRPTW, customer should be visited in a time frame; PDP and HVRP, a heterogeneous fleet with vehicles with different capacity. It depends if it is a single or a multiple depot; homogeneous or heterogenous fleet; existence of time-windows, and so on.
constraints of vehicles are respected, this objective function can be the minimization of all traveling costs, the maximization of the number of served customers, or some combination of these or other factors.
2.3.3 Multi Routes and Time Windows Problem
Macedo et al. (2011) proposes a new algorithm that is based on a pseudo-polynomial network flow model, represent discrete time instants and whose solution is composed of a set of paths, each representing a workday. In this paper there is a single depot and homogeneous vehicles and the objective function translates the fact that it is always desirable to visit as many customers as possible.
Osvald & Stirn (2007), study MVRPTWTD where the times between two locations depends on both the distance and on the time of the day. This was applied in perishable food on the Slovenian vegetables market. In the VRPTW we know location, the demand and the delivery
window. Here if the time window was violated there is a penalty cost but it is not allowed a
hard time windows for the depot. The new network model presented for MVRPTW solved with CPLEX, the algorithm was tested and compared with branch-and-price algorithm and used the same set of instances and the same values of parameters. Osvald & Stirn (2007), on their study, firstly used a sequential constructive heuristic that solves a classical VRPTW, second introduced a tabu search, which is a local method that uses memory structures.
2.3.4 Heterogeneous Fleet Vehicle Problem
According to Grı Koç, Bekts, Jabali, & Laporte (2015) , HVRP generally consider limited or an unlimited fleet of capacited vehicles, where each has a fixed cost, in order to serve a set of customers with known demands. There are different types of vehicles, one depot and a set of customers, as a NP-hard problem Wang, Li, & Hu (2015), use to solve a modified Clark-Wright route construction heuristic and two, a ruin-recreate heuristic and a threshold tabu search. Wang et al. (2015), introduce Solomon´s instances and adjust to fit in a real case study, a supermarket chain in China. In the literature review there are many approaches to VRP, but the real cases are for perishables, omitting cases of shipping non-perishable goods, so it is a gap that could enhance profit to retail companies that work with non-perishable goods. In this case involving heterogeneous fleets, a single deposit, various stores, time windows there are some gaps regarding the application of these variances. It is necessary to
develop more studies that merge these variances to optimize the operation - Shipping - and minimize the costs of transport routes.
Anand Subramanian a,b, Puca Huachi Vaz Penna d, Eduardo Uchoa c, & Luiz Sat, n.d., consider the existence of different vehicle types, with distinct capacities and costs and want to determine the best fleet composition, the set of routes that minimize the total costs. They studied five variants involving limited and unlimited fleet with fixed and or variable costs were considered, to solve this type of problem they proposed a hybrid algorithm composed by an Iterated Local Search based heuristic to limited and to unlimited (Fleet Size and Mix) fleet. In cases like this, it is not easy to find an optimal solution because of the complexity of the problem and it is a multi-objective optimization problem. Ehrgott, Ide, & Schöbel (2014), explain that in real-world applications optimal solutions are often of limited value, because disturbances of or changes to input data may diminish the quality of an optimal solution or even render it infeasible. So, this study tries to gain insight into the new area of robust multi-objective optimization, merging robust (single multi-objective) and deterministic (multi-multi-objective optimization). They provide three methods to minmax robustness to be extended to multi-objective optimization problems.
Mancini (2015), introduce a VRP with heterogeneous fleet and with a multi depot problem. Here a limit on the maximum route duration is imposed, and not every customer will be served by all the vehicles or from all the depots. It proposes an Adaptive Large Neighborhood Search (LNS) metaheuristic approach followed by digital results, pertaining to realistic instances, which show the effectiveness of the method. Like most of the papers, the goal is to carry out delivery operations at the minimum costs, while respecting constraints due to driver scheduling and customer/vehicle compatibilities. This approach brings innovations in the capability of exhaustively exploring a large neighborhood in a very short computational time, so this LNS framework is more effective than the traditional LNS.
Leung, Zhang, Zhang, Hua, & Lim (2013), introduce another variant of the classical VRP is the two-dimensional loading heterogeneous fleet vehicle routing problem (2L-HFVRP), which fleets have different capacity, fixed and variable operating costs, length and width in dimension and two-dimensional loading constraints. As several others studies the objective is to minimize transportation cost of set of routes in order to satisfy customers demand. They use a simulated annealing with heuristic local search to solve the problem and the search was then extended with a collection of packing heuristics to solve the loading constraints.
Once more, Leung et al. (2013) addressed a NP-hard for 2L-HFVRP and solve with heuristic local search but realize that it could also be capable to solve 2L-CVRP with a good set of results. In this study was missed the time-window factor.
Y. Chen, Hao, & Glover (2016), contribute to the Capacitated arc routing problem (CARP) with a Hybrid Metaheuristic Approach (HMA), which incorporates an effective local refinement procedure, coupling a randomized tabu thresholding procedure. HMA showed the ability to identify either the best known results or improved the best known results for almost all currently available CARP benchmark instances.
Many heuristic approaches were submitted over the years, such as a “packing first, routing second” heuristic approach that reported 46 VRLP instances. Bortfeldt & Homberger (2012), analyze, if routing and packing should be tackled, in the Vehicle Routing and Loading Problem (VRLP), which combine vehicle routing, time-windows and three dimensional loading.
Low, Chang, Li, & Huang (2014), focus on a production scheduling with delivery problem, although they studied the delivery of the goods to retailers instead of to the customers (or stores), there is based on determine the sequence of a vehicle (heterogeneous fleet) respecting the time windows. It was applied a non linear mathematical model to minimize the total cost (transport, vehicle arrangement cost, penalty costs). To solve the problem, they used two adaptive genetic algorithms (AGAs), and the computational results were evaluated through randomly generated test problems in various environments.
H.-K. Chen et al. (2009), propose a nonlinear mathematical model to a scheduling vehicle routing problem with time-windows but for perishable food. In contrast to others studies this has the objective to maximize the expected total profit of the supplier. Here they elaborate a solution algorithm composed of the constrained Nelder-Mead method and a heuristic for the vehicle routing with time window to solve the complex problem, the results show that this algorithm is effective and efficient. They conclude that production scheduling and vehicle
routing for perishable goods are integrated into a unified framework which is also applicable to the fields like food, vegetables, flowers, living animals and so on.
In conclusion, there isn´t an unique methodology to solve a VRP with time-windows, heterogeneous fleet and one depot as variants for shipping non-perishable goods. Regarding to this thesis it will be important to unify methodologies to find the best solution to this problem. In the next section, we will summarize the main contributions and results of papers that most supported the writing of this thesis.
2.4 Presentation of findings
Authors Citations Methods Results/Contributions
Anand (Anand Subramanian a,b et al., n.d.)
The objective is to determine the best fleet composition as well as the set of routes that minimize the total costs.
HFVRP using Iterated Local Search (ILS) based heuristic and a Set Partitioning (SP) formulation.
They determined the best fleet composition that minimize the sum of fixed and travel costs.
The hybrid algorithm was tested in 67 benchmark instances with up to 360 customers and it was found capable to obtain 8 new improved solutions, to equal the result of 54 instances and failed to obtain the best known solution of only 5 instances.
(Bortfeldt & Homberger, 2012)
The main idea of the heuristic is to separate packing boxes in loading spaces and constructing routes from each other in order to structurally reduce the packing effort and to thus obtain an efficient heuristic method.
Vehicle Routing with Time Windows
and three-dimensional Loading
(VRLP) using a two-stage heuristic
packing first, routing second.
They achieved high quality results for 46 VRLP instances by Moura and Oliveira.
Song, Byung
Duk; Ko,
Young Dae
Managing the delivery of food products because of the customer satisfaction issues coming from the
A nonlinear mathematical model and a heuristic algorithm to generate efficient vehicle routings with the objective of
Comparing the use of refrigerated and general-type of vehicles for multi-commodity perishable food products delivery, the average number of served
freshness of delivered food products.
maximizing the level of customer satisfaction.
customers per each route by refrigerated-type vehicle tended to be greater than that of general-type vehicle duo to the constraint of the minimum customer satisfaction.
Wang, Zheng; Li, Ying; Hu, Xiangpei
A HVRPTW-ILC can be defined as an undirected network with single depot a set of n customers. Two types of vehicles refrigerated and non-refrigerated and three types of goods stored in the depot.
A heterogeneous multi-type fleet
vehicle routing problem with time windows and an incompatible loading constraint using a mathematical model, a ruin-recreate heuristic algorithm and a threshold tabu search method.
Wang investigated in a real supermarket chain, Lehaha Supermarket, in Dalian city of China to
prove feasibility and effectiveness. Their
contribution is huge because HVRPTW-ILC is not very much studied in the literature.
Osvald Ana;
Stirn, Lidija
To minimize the overall distribution cost, the objective function must not only model the number of vehicles, the total distance-traveled and the total travel-time, but additionally the loss of quality of the load.
A Vehicle Routing Problem with Time Windows and time-dependent travel-times using a heuristic approach based on tabu search and verified using modified Solomon’s problems.
Osvald applied in Slovenian food market giving improvements of up to 47% reduction in perished goods. They studied the quantification of quality loss in perishable goods. When time-dependent travel-times were taken into account the savings increases on average to 40%.
Chen,
Huey-Kuo; Hsueh,
Che-Fu
The objective of this model is to maximize the expected total profit of the supplier.
A nonlinear mathematical model to consider production scheduling and vehicle routing problem with time windows for perishable food products
Using Visual C++ 6.0 based on Solomon’s problem set. This algorithm solve PS-VRPTW-P efficiently and returns a reliable solution for production scheduling and vehicle routing problems for
(PS-VRPTW-P) using the Nelder-Mead methos for solving nonlinear optimization and applied to non-convex problems.
perishable goods under stochastic demands.
Macedo, Rita; Alves, Cláudio
The problem consists of finding the best set of routes, according to a given objective function, such that all operational constraints of the vehicles are respected, and the set of customers is covered.
For a VRPTW problem they used an iterative algorithm that relies on a
pseudo-polynomial network flow
model with a homogeneous vehicle.
This method is able to solve more instances than the exact method described in literature.
Amorim, P;
Gunther, H. O.
In the first objective, total costs are minimized, namely: production costs, transportation costs and spoilage costs. (…) This objective function aggregates the measurable economic importance throughout the considered supply chain.
A multi-objective framework was used for two types of perishable goods: with fixed life and with loose shelf-life.
As an exploratory research in this field, they realize that in the fixed shelf-life case for a 70% mean remaining shelf-life of delivered products reach savings around 42%.
3 Problem Characterization
As shown in figure 2, to better understand the problem we should understand the currently reality and then make a description in order to know the important data to collect for the model formulation. After select the method we could validate the model and then implement the solution found.
Figure 2 – Several steps to find a solution to the problem.
Therefore this chapter describes the company; explains the current situation of warehouses; how they operate separately and jointly and how they will proceed at the new warehouse.
3.1 Company´s Description
Jerónimo Martins is a Portuguese company with 200 years of history. In 1980 they established a strategy for the supermarket segment and recovered the original activity: food distribution. The main activity is Food Distribution through supermarket chains (Pingo Doce) and cash & carry (Recheio) in Portugal, food stores in Poland (Biedronka) and Colombia
(Ara). Although the company has various business areas, we will focus our attention on Jerónimo Martins Retalho (JMR).
JMR is primarily engaged in the distribution of non-perishable and perishable goods to their supermarket chains: Pingo Doce and Recheio. The company has a market position in Portugal for its low prices’ policy, strengthening the value proposition and the quality of its goods. They are also involved in various activities: ordering, purchase, transport and storage.
During this thesis we will look to JMR Warehouses in north of Portugal that focuses its activity in the cities Guardeiras (Stock), Freixieiro (Stock) and Laúndos (JIT) where they have the three warehouses for non-perishables goods. In Appendix B, is represented the process map of non-perishable goods, describing the management, core and support processes.
3.2 Routes
Routes can be described as a graph where the warehouse and the stores are the vertices and the roads are the arcs. Each arc has an associated value that represents the distance traveled (between the warehouse and the stores) and the time of travel.
The routes have restrictions: total orders of the stores must be equal to or less than the capacity of the fleet and take into account the time-window of stores. For the company the costs of transports are very high, so is helpful to minimize distances and the time spent on the shipping (the warehouses to the stores). To calculate the cost of the routes is necessary to take into account the price of kilometers, fixed costs of each fleet and the distance traveled (help to know latitude and longitude from warehouses and stores), as shown in the Appendix C, D and E.
3.3 AS-IS (Current situation)
Currently there are three warehouses for non-perishable goods and they are distant from each other. Guardeiras warehouse distance 5 km from the Freixieiro warehouse and 26 km from the Laúndos warehouse. As the goods are distributed in the three warehouses is necessary to develop different routes and joint routes. Joint routes implies that the trucks go to one of the warehouses (Laúndos or Freixieiro) collect certain amount of pallets and turn to Guardeiras
effort implies that the truck makes a change on the route (increasing the number of kilometers), wastes time on loading and unloading at two different warehouses before getting to the stores’ destination. Nowadays, non-perishable warehouses are dependent on perishable warehouses (goods as fruit, fish, fresh food and frozen food), because the truck fleet of transport is used by all warehouses.
JMR has a strong internal dynamics between the warehouses: Stock and JIT, transport, carriers and stores, to achieve the goals successfully. JMR also knows that its good performance depends strongly between the relationship with its stakeholders, in Appendix F, is shown a workflow diagram with these interactions.
3.4 Organization of warehouses facilities
At this moment it is important to clearly define the dynamics of JIT and Stock warehouses and transport, since it depends on the success of operations. The warehouses divide their tasks by reception, executing and shipping teams.
Each warehouse has gates (are used to receive or ship goods), which are currently divided into four lines, which means greater space. However, certain stores occupy the four lines (the whole gate) depending on pallet volumes. Each lines holds up to 11 pallets or 22 half pallets. It is important to explain that each pallet stores an average of approximately 55 units (height up to 1.80 meters) and half pallets approximately stores approximately 25 units, and after finished are wrapped in plastic film (either manually or with the robot itself).
Currently, the volumes produced at warehouses are shown in the table 1 below.
Stock Warehouses JIT warehouse
Average Guardeiras Freixieiro Laúndos Total
Boxes/year 20 722 119 1 413 225 35 215 714 57 351 058
Boxes/day 66 000 4 530 97 900 168 430
Pallets/year 370 648 135 003 640 285,71 1 145 936,7
Pallets/day 1 210 433 1 780 3 423
The reception team receives the goods either by suppliers, backhauling or transshipment, ordered by stores, register them in the system (give input and put labels with product information and barcode) so then can be carried or stored, as we can see in Appendix G. The execution team, in all of the warehouses, has the task of assembling the pallets for the stores, according to information provided by the system of requests from the stores.
The shipping team is in charge of moving the pallets produced by the execution team to the gates, to be shipped to stores.
The Transport team provides a map to the shipping team, with the daily planning of delivery of pallets per store and route (which stores are delivered together in the same truck).
While the JIT warehouse features as approved condition and ships within 24 hours all the items, the warehouse Stock besides receive and send, store items (stock). Next we will explain deeply each warehouse operations.
3.4.1 JIT Warehouse
The JIT warehouse, in the current context of the company, dispatches from Mondays to Fridays since 2 p.m to 12 a.m and since 2 p.m. from 11 p.m on Saturdays, in three shifts: 6 a.m to 3 p.m; 2 p.m to 11 p.m and 10 p.m to 7 a.m. Suppliers come to warehouse to unload the goods of the day, which are checked and compared to the ordered, by the reception team. In Appendix H, it is shown the workflow diagram of the suppliers into the JIT warehouse. After reception, goods are put in the system, to await for further handling.
This warehouse has a specific layout divided by spaces for each store, there the pallets are performed on the ground by the picking operators according to previous instructions and when finished wrapped in plastic film. After this, the pallets begin to be displaced (by the shipping team) to the pre-load zone or immediately to gates.
If by any reason (delay of the dispatch, overflow of goods, end of the working day,…) some of the pallets of the JIT warehouse are not shipped, they are added to the Stock warehouse load and sent to the respective stores. In Appendix I is shown the process map of shipping in JIT warehouse.
3.4.2 Stock Warehouses
Stock warehouses (in Guardeiras and Freixieiro) have the task of storing goods, mainly their own brands (Pingo Doce and Amanhecer), on shelves sorted by date. They work 24 hours from Monday to Sunday until 1 p.m, divided into three shifts. The Warehouse in Freixieiro just stores a few items because of its small size; it is a backup for Guardeiras warehouse. The Stock warehouse in Guardeiras, receives pallets from JIT and Freixieiro warehouses in the afternoon and add them to their load as previously referred. In Appendix J is shown the Stock warehouse’s operations before shipping.
3.4.3 Stores description
At this moment, the shipping is made to 168 stores (Pingo Doce and Recheio). During this study we will present data from just 162 stores, because the others stores are too recent and no historical data were available. There are three types of delivery in stores:
- Those that are supplied during the day, normally 84 stores (JMR called wave 1 to identify which stores are dispatched first) and sometimes 17 stores (when there are free gates and the pallets are already executed, stores can be stocked ahead of schedule, called anticipation); - Those that can be supplied over night (normally 109 stores, if the 17 stores are supplied in advance no longer count);
- The key stores (drivers have access to the key and leave the goods in the store without no one to receive them).
Each store has a predefined time-window (half-hour for each) for delivery, so employees can organize themselves to receive and store the goods in the store. For example, Pingo Doce Grijó’s time window is 20:30/20:59. In Appendix K, there is represented the time-windows of the different stores. The setting of the time-window is related to the characteristics of stores: the reception docks, the number of employees, if it has an antechamber (that works like a second store warehouse) or if the store is in a residential area. But not always this time-windows is accomplished, often there are delays in deliveries. In this cases, the goods can be out of stock in stores and overflow the warehouses blocking new deliveries and delaying shipping processes.
We must refer that not every store can receive all types of trucks, there are a few of them that have some constraints, on Appendix L we can verify each type of truck can be receive by the stores.
3.4.4 Transport Team
The warehouses receive the demand of each store and for that this delivery is always planned 24 hours in advance. Therefore, each warehouse sends to the transport team a daily forecast of the number of pallets per store for the next day, JMR transport team coordinate truck fleet and plans the route (to stores) of the trucks a day in advance, having to make slight adjustments during the day in the operation. The transport team plans depending on the inherent constraints (type of trucks, time-windows of stores; existing fleet) and according to the registration number of each truck, which route will be taken the next day.
JMR works with two carriers ZAS and TJA, in table 2, is described capacity of different types of trucks.
Carriers
Type of truck fleet ZAS TJA Total
Trailers (33 pallets) 23 9 32
24 pallets 18 - 18
22 pallets 33 18 51
12 pallets 11 - 11
Total 85 27 112
Table 2 – Capacity of the fleet of trucks.
ZAS has a fleet of 85 trucks and 188 drivers 24 hours available and is an exclusive company of JMR. TJA has 27 trucks and 60 drivers available 24 hours (not exclusive JM). Each driver works for 9 hours and in average makes 2 routes (from warehouse to stores and back to warehouse, twice a day). The truck fleet is in warehouses and operates 24 hours, travels to the set routes to taking the goods to stores intended. At the end of this journey trucks return to the
Each truck has installed a routing system control that provides an alarm (advice) if the driver arrives late to the store or if the truck diverge from the planned route (using the motorway instead of national roads; change the order of stores, etc.). It also has sensors that locate the truck if it is in the store or warehouse. Each load takes 30-45 minutes on average and if the truck is a trailer (33 pallets) takes up to 1 hour. In case of unloading the trucks, both in the warehouse and in store, takes 30 minutes and if is a trailer up to 45 minutes.
Normally, routes are planned to supply the biggest stores (Recheio), to furthest stores (IP4 and IP5) and then to the nearest stores. The transport team also decides how to make store transfers to other stores for excess stock, or to the warehouse stock and, when drivers have to collect in stores rollcontainers, pallets, risk boxes and return to the warehouse.
The daily counting of kilometers is made in the next day for adjust if any route was changed. The distribution per store is assigned to a number registration, so if there are changes have to be made in the warehouse (in loco), not by the system.
The profitability of transport happens when the percentage of occupancy of the truck is 100%, but the actual average is far away from that, as represented in Appendix M.
Transport team is starting to use the tool Transport Management System (TMS), but is still in testing mode, when TMS implementation is completed it will be an important tool for planning routes using real quantities. The TMS with the introduced variants (warehouse-store and store-store distances; consider the load time in the warehouse, the unload time in the store and the time to return to the warehouse) will help to define the set of routes should each truck go to each store.
3.5 TO BE situation - New Warehouse
In order to unify its warehouses of non-perishable goods, the company is building from scratch one new warehouse which will join all types of non perishable goods (JIT and Stock). It is easily concluded that the advantages are huge because of the fact that, the warehouses being currently far away from each others, implies greater costs and loss of time. It will also allow greater flexibility in the operation (fewer people, fewer processes, less charges), creates synergies in teams and also with resources.
The new warehouse with 70 000 m2, will integrate the three existing warehouses of non-perishable goods. It will have 24 gates dedicated to the JIT layout and 73 gates for the Stock layout. The increased space will decrease the transhipment and improve the capability of
organization, storage and pick up of the goods in the layout, therefore saving time. The gates will be at both sides, in one side to receive the goods, and the other side to send the goods to the stores. Non-perishables will be divided into food and non-food goods in each layout. These new settings will save time in the executing of pallets and consequently on their shipping. It would be important too, manage the entropy with drivers inside the warehouse, like avoid passing the discharge lines and be kept to their destinated gates.
With the aim of providing a even more efficient response to shipping non-perishable, this model will help improve the overall efficiency of all these processes. Figure 3, represents the new warehouse, the different layout of it and its organizations.
4 Model Development
4.1 Quantitative Methodology
4.1.1 Comparative analysis of existing approaches
Management Science, operations research and decision science are connected to quantitative analysis. We should understand and define the problem, decide the set of alternative solutions, determine the criteria that should be used to evaluate the alternatives. After evaluating them we choose the best alternative and implement it.
Quantitative approach is associated to data analysis of the problem and developing mathematical model to describe the objective function, constraints and the connections between all variables. So, for complex problems that involve high financial investment, this type of implementation can help to save costs and time to the company. It was important to understand the problem and then adequately structured mathematically to find solutions. For model development we could use representations of real situations or object: iconic models (a real model of the objects), analog models (similar but do not have the same physical appearance as the object being modelled) and the last one, the use of symbols and mathematical relationships or expression to represent the problem.
The use of models helps to understand the situation and if it helps to avoid bad decisions or losing money. The third model was considered the most apropriated in this particularly problem, so it was used to define an objective function to minimize the costs and define a set of constraints. For decision making the critical aspect it is formulate and expressed correctly the objective function, constraints and their relationships.
Aiming to transform information into knowledge contributing to fulfill simple or complex tasks, using DSS helps a greater organization of data and its treatment which allows the decision maker to have a more coherent decision. Nowadays the rising costs of fuel is harmful to businesses that depend on transport. The use of DSS allows the company to choose the best route taking into account a set of criteria and restrictions. Thus, it will be expected that decision makers are able to do a better fleet management and give a better informed response to this multidimensional problem. This system does not totally eliminate the role of the manager as there are elements of the problem not possible to be model (daily
unpredictability), however the use of this type of system that favours decision-making is faster and supported by data.
The method used in the project is a quantitative approach called Vehicle Routing Problem after the formulation and description of the problem remains choosing the models and algorithms suitable for solving this problem.
In this work, the constructive heuristic, is intended to know which route should be chosen to minimize the cost of transportation and ensure delivery. So, three heuristic approaches called Pseudo-code of Priority-based, Ruin and Recreate Heuristics and Large Neighbourhood Search algorithm are used.
4.1.2 Method used in the project
The method is an oriented plan of work which aims to certain objectives and that leads to the research process. The quantitative method involves collecting and analysing numerical data in order to explain, predict and control phenomena. It is linked to experimental research and tries to find the relationship between variables, making descriptions and test theories. In this case, the method is based on the literature review.
The classical transportation model is characterized by a set of trucks each with known capacities; a set of demand locations each with known requirements and the unit costs of transportation between warehouse to stores. This difficult combinatorial problem conceptually lies at the intersection of these two well-studied problems: The Multiple Travelling Salesmen Problem (MTSP) and The Bin Packing Problem (BPP). MTSP: that ensure k vehicles, with minimum cost routes, visit at least one store and each store is visited exactly once. BPP: The question of whether there exists a feasible solution for a given instance of the VRP is an instance of the BPP, in which all edge costs are taken to be zero (so that all feasible solutions have the same cost). Hence, we can think of the first transformation as relaxing the underlying packing (BPP) structure and the second transformation as relaxing the underlying routing (TSP) structure.
In this research is used VRP that concerns to the shipping process of non-perishables goods, using a single depot, a set of routes performed by a fleet of trucks. The routes start and end in the depot after being in stores to satisfy their demands. A constructive heuristic approach
value of profit and the process continuous until there is no more capacity in all trucks or using metaheuristics (tabu search or genetic algorithms) we could reach a quality.
Real life problem presents a high degree of complexity, special concerning multi-dimensional variants (vehicle capacity, time-windows, …) so we must use approaches to find feasible solutions. Is important to find robust and efficient tools in order to determine a valid solution.
4.2 Problem Formulation
In this study there is a problem of shipping non-perishable goods (p) from the warehouse (V0) to stores. The new warehouse will be divided in two types of layout: JIT and Stock.
A graph is a type of diagram constructed to make possible the visualizations of the relationships (arcs) between the entities involved (nodes). The stores are distant from each other and from the warehouse, a direct graph G = (V, A), where V = {0,1,..,n} is the set of n+1 nodes that represents stores and A the set of arcs. Node 0 corresponds to warehouse and the others nodes set V´=V\{0} represents n stores. Each store iV´requires a supply of qi volumes from warehouse. There is a heterogeneous truck fleet (K), with M = {1, 2, 3 e 4} with certain capacity (KT - it could have 12, 22, 24 and 30 pallets) to take the goods to stores. We must supply all the stores with minimum costs, so is important to save kilometers and put maximum charge into the trucks. Each vehicle type has associated a fixed cost, equal to fk. So each arc
i, j A and each vehicle type kM has a positive routing cost ckij. A route is represented by (R, k), where R = (i1, … iR), a simple circuit in G containing the warehouseand each k used with the route. R will refer both to the visiting sequence and to the set of stores of the route. A route (R, k) is feasible if the total demand of the stores visited by the route does not exceed the vehicle capacity. The cost of a route corresponds to the sum of the costs of the arcs forming the route, plus the fixed cost of the truck associated.
In a VRP problem there are feasible solutions that guarantee minimum total cost, each costumer is visited by exactly one route and the number of routes performed by truck kM
is not greater than mk.
Currently, planning is based on the distances to the stores (geographic location), type of truck that could go to that store, time-window of the stores and the volumes that are accurate transport. The initial priority is given to the biggest stores (Recheios) and also to stores that
have greater distances to make and there are formed clusters (if the truck’s capacity is enough to supply more than one store). Stores have a time-window so unload the pallets have to be made at these times.
We could organize the data set in input data: number of stores; order request from stores; truck capacity; distance between warehouse and stores; delivery transportation cost; truck fixed costs; delivery time for each store; number of trucks and output data: prediction and analysis result of estimated costs and store satisfaction and arrangement of product delivery for each truck.
4.2.1 Sets nodes store of Set V trucks all of Set K truck of type general of Set KT goods perishable non of Set P j node and i node between on satisfacti store SSijK 4.2.2 Parameters k truck at i store of Time Service quired sik Re i node at store by ordered pallets of Volume pi warehouse in K truck of time eparation tK Pr ts service i cos t routing cijk cos truck each of ts fixed fk cos truck each of capacity mk operation each at K truck of time delivery Maximum tk
4.2.3 Decision Variables:
If there are n related quantifiable decision to be made, they are represented as decision variables whose respective values are to be determined.
K truck by served is i node at store that indicating iable decision Binary yiK var served is i node of customer after directly visited is j node at customer the wether indicating iable decision Binary xij var
j store to going before store from warehouse the to return o that truck that indicating iable decision Binary xi0j var 0 store each to transport truck each pallets of number ki
0,1 var iable decision ykj 4.2.4 Mathematical ModelAs Hillier (1990) says, mathematical models have many advantages over a verbal description of the problem. One obvious advantage is that a mathematical model describes a problem much more concisely.
At the beginning we thought it was important to analyze what would be the impact of the store to receive or not receive the required goods, and as such, our objective function would be to maximize the satisfaction of the store. The satisfaction of the store is measured by ensuring that the goods are daily shipped to every store. If not, the store is penalized by the lack of goods.
This model should maximize the store satisfaction, with the objective function:
Maximize:
k i k i k i Stock JIT SS y Z Such that: (1) , 1,...,162 118 1
i y p ki ik k i these sum represent the possibility to have more than one truck to serve store i over the total time of loading the stores.
(2)
V i j i j V x0 1, (3)
V i i j j V x 0 1, (4)
V i iV i i x x0 0,guarantees that number of direct connection between warehouse and all stores and reciprocally are equal.
(5) xi0 x0j 2.xi0j (6)
k k k i i V y 1 , 1 (7)
k k ij k j k i y x i j V y 1 , , (8) x y x yik k V i iV i k i i
, 0 0 ,Number of times that each truck leaves warehouse equals number of times it returns.
(9)
tik si ti xi
tk j V k V iMax
, , max 00 , the store that has the maximum sum of start
time of the service, service time and travelling time between store and warehouse is always smaller that a given time for delivery. Notice that start time of delivery, k
i t , already includes the time to travel to node i, independent of the path it took to reach i.
(10) tik si tij M(1xij)tkj, i,jV,k
for each truck, in case we don’t go through the path that links i and j directly, but still go to both i and j stores, we want to subtract some time M to the sum of the service time, the travelling time between i and j and the start service time in store i, but only if we go through the direct link between i and j. Otherwise, we do not subtract any time. In the end we have to guarantee that this time is still smaller than the overall time in takes to reach store j.
